Hello, Shadow_penguin990, and welcome to TSC!
Reading the FAQ would help you with the basics of competition here. Basically, you submit times/scores/ring counts/whatever for any game we currently hold competitions for (no cheating, btw! We don't tolerate that here). After a time, your submissions are added unto the database and compared with other submissions for that division (e.g., Sonic 1/Times/Green Hill 1 or Sonic 3/Rings/Angel Island 1/Tails). For every rank away from 1st that you are, you are given a point. If you have no submission for a particular division, you are given a number of points equal to the current number of submissions for that division. Thus, if you have 1st in every division in a game, you will have 0p (which is what the best strive for, though it is rarely accomplished).
...eh, I think I made that sound complicated. Maybe you should just read the FAQ and make another post if you still have questions... >_>